Where Do These Speeds Come From?

[h2ouniverse]

1) indeed omega is not the same in both diagrams; this is to illustrate the parallel between both problems, not to claim full identity; this is fully exact in the "relative rotation" case; and an analogy in the "relative translation" case. But...<br />2) D is an equivalent distance equal to square root of Izz/m for the rotation case. D=R for a cylinder or a ring. But for a homogeneous sphere D=Rsqrt(2/5). It represents the RMS average of distance between the elementary masses constituting the object and the axis of rotation. It is a measure of the spatial distribution of the object's mass. The analogy I propose to better feel the issues is to consider a "D" for the other pb by positing D=I(u,u')/m, with u and u' the two directions of spacetime about which the "rotation" occurs; I(u,u') would be a momentum of inertia. For rotation in first case that is in plane x,y and the complementary directions are u=z, u'=ct. For the translation case this is in plane x, ct so u=y and u'=z. <br />Note that such D has a real physical meaning in relativity context. Imagine your object is a ring of radius R and axis z. Then D=R. But to stop the motion of such object you need to influence the matter of the ring, commanding from the center. In relativity theory, this cannot occur before a minimum time that is propagation of your actuation at best at speed c. And this minimum time to reach the matter of your object is t1 = D/c. So D represents also the height of the causality cone in the x, ct diagram. Your action to merge the two referentials in the "relative translation" diagram cannot occur in effect before time t1, that is a spacetime distance of ct1 = D! So you can measure the "alpha" angle both and consider the D-radiused circle. For a non-cylindrical object, D and t1 represent RMS averages. Using t1 to normalize t leads to consider ratios t/t1 = ct/D.<br />3) in your example, you do not show one translation and one rotation but two rotations that are fully identical in nature, with

 

[emperor_of_localgroup]

I think this time I found the real problem with the equations. If you equate kinetic energies (KE), ie, KE(translation)=KE(rotation), and use inertia about axis of spinning (as opposed to axis of revolution), you wind up with the relation between D and R (equation 1 in the pic). Simple substitution I=mD² makes D < R for a sphere, meaning axis or rotation is inside the sphere, not even the center of the sphere. Note, the substitution does not cause any problem for a RING or a Cylinder or a Circular plate. <br /><br />Correct formula for inertia for the earth should be equation 2 in the pic considering its spinning and revolution about the sun. <br /><br />I'm still struggling to understand your reason to align 'time axis' and the meaning of alpha when it comes to time axis. Alignment of (x,y) axes and there relation to alpha are understandable. <div class="Discussion_UserSignature"> <font size="2" color="#ff0000"><strong>Earth is Boring</strong></font> </div>

 

[emperor_of_localgroup]

These are our logical speculations. Your off the wall idea about string and earth motion gave ME an off the idea. Here is my thought.<br /><br />May be Einstein didn't go far enough and we need another Einstein to show us the exact shape(s) of curvatures of space-time caused by gravity, specially when two curvatures interact. May be our earth (or any planet, satellite) is traveling in a space-time ditch, a circular space-time ditch around the sun like a circular rail track. A space-time ditch or a space-time groove, whatever you call it, may be the reason why it is so hard to derail it, not that we are complaining.<br /> <div class="Discussion_UserSignature"> <font size="2" color="#ff0000"><strong>Earth is Boring</strong></font> </div>

 

[thamior]

*laughs* I'm glad that it did some good. I was actually expecting it only to cause chaos or a bunch of "Thamior's a lune" rumors to start spreading, lol. <div class="Discussion_UserSignature"> <p>--What is the truth but a wisp of truly un-attainable information.  There is no absolute truth anyways, only false perceptions and misgivings.--     </p> </div>